Question

2．脫式計(jì)算，能簡(jiǎn)算的要簡(jiǎn)算．
$\frac{8}{13}$÷7+$\frac{1}{7}$×$\frac{6}{13}$
$\frac{4}{7}$×$\frac{1}{4}$+0.25×$\frac{3}{7}$+$\frac{1}{4}$
$\frac{1}{5}$÷[（$\frac{2}{3}$+$\frac{1}{5}$）×$\frac{1}{13}$]．

Answer 1

分析 ①$\frac{8}{13}$÷7+$\frac{1}{7}$×$\frac{6}{13}$，把除數(shù)轉(zhuǎn)化為乘它的倒數(shù)，再運(yùn)用乘法分配律簡(jiǎn)算；
②$\frac{4}{7}$×$\frac{1}{4}$+0.25×$\frac{3}{7}$+$\frac{1}{4}$，把0.25化成$\frac{1}{4}$，運(yùn)用乘法分配律簡(jiǎn)算；
③$\frac{1}{5}$÷[（$\frac{2}{3}$+$\frac{1}{5}$）×$\frac{1}{13}$]，先算小括號(hào)里面的加法，再算中括號(hào)里面的乘法，最后算除法．

解答 解：①$\frac{8}{13}$÷7+$\frac{1}{7}$×$\frac{6}{13}$
=$\frac{8}{13}×\frac{1}{7}+\frac{1}{7}×\frac{6}{13}$
=（$\frac{8}{13}+\frac{6}{13}$）×$\frac{1}{7}$
=$\frac{14}{13}×\frac{1}{7}$
=$\frac{2}{13}$；

②$\frac{4}{7}$×$\frac{1}{4}$+0.25×$\frac{3}{7}$+$\frac{1}{4}$
=$\frac{4}{7}×\frac{1}{4}+\frac{1}{4}×\frac{3}{7}+\frac{1}{4}$
=（$\frac{4}{7}+\frac{3}{7}+1$）×$\frac{1}{4}$
=$2×\frac{1}{4}$
=$\frac{1}{2}$；

③$\frac{1}{5}$÷[（$\frac{2}{3}$+$\frac{1}{5}$）×$\frac{1}{13}$]
=$\frac{1}{5}÷$[$\frac{13}{15}×\frac{1}{13}$]
=$\frac{1}{5}÷\frac{1}{15}$
=$\frac{1}{5}×15$
=3．

點(diǎn)評(píng) 此題考查的目的是理解掌握分?jǐn)?shù)四則混合運(yùn)算的順序以及它們的計(jì)算法則，并且能夠靈活選擇簡(jiǎn)便方法進(jìn)行計(jì)算．